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Math 4 Unit 6 Final Exam Review

Total questions: 20

Worksheet time: 5hrs 0mins

Name
Class
Date
1.

Is this a probability distribution?

a)

No, the sum of p(x) does not equal 1.

b)

Yes, all p(x) are between 0 and 1.

c)

No, all p(x) are not between 0 and 1.

d)

Yes, the sum p(x) is 1.

2.
A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?
a)
0.20
b)
0.29
c)
0.39
d)
0.61
3.
a)
Yes, because all of the probabilities are between 0 and 1 inclusive and the sum of all the probabilities is 1.
b)
No, all probabilities are not be between 0 and 1 inclusive
c)
No, the sum of all the probabilities is not 1.
d)
Yes, because the distribution is symmetric
4.

434 Company pack coffee in bags marked as 250 g

A large number of packs of coffee were weighed and the mean and standard deviation were calculated as 255 g and 2.5 g respectively.

Assuming this data is normally distributed, what percentage of packs are underweight?

a)

2.5%

b)

3.5%

c)

4%

d)

5%

5.

Students pass a test if they score 50% or more.


The marks of a large number of students were sampled and the mean and standard deviation were calculated as 42% and 8% respectively.


Assuming this data is normally distributed, what percentage of students pass the test? in percentage...

a)

5

b)

16

c)

24

d)

32

6.
Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Do not replace the card. Repeat the process 5 times. Let X = the card you observe.
a)
Yes
b)
No, the trials are not independent.
c)
No, there are more than 2 outcomes
7.
Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.
a)
Yes
b)
No, the trials are not independent.
c)
No, there are more than 2 outcomes
8.
Which of the following is false about binomial probabilities?
a)
Their distributions are approximately symmetric.
b)
Trials must be fixed.
c)
Events musts be independent.
d)
The probability of success must be 0.50
9.
Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6
a)
14
b)
4.67
c)
5
d)
7.5
10.
If the expected value is negative, are you expected to win?
a)
yes
b)
no
11.

Find the mean (expected value) of the probability distribution.

a)

85

b)

83.2

c)

87.1

d)

84.4

12.
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? 
a)
1084 to 1216 pounds 
b)
1106 to 1150 pounds 
c)
1106 to 1194 pounds 
d)
1128 to 1172 pounds
13.
A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.
a)
2.5%
b)
.15%
c)
2.35%
d)
2.25%
14.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?
a)
68%
b)
99.7%
c)
95%
d)
84%
15.

What is the purpose of z-scores?

a)

to describe the exact location of a score within a distribution

b)

to find the mean of the distribution

c)

to describe the shape of the distribution

d)

to find the standard deviation of the distribution

16.

What is the formula to find the z-score for population?

a)

z=X-M

b)

z=σ-M/μ

c)

z/M=μ

d)

z=X-μ/σ

17.

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

a)

True

b)

False

18.

Find the Z-score.

Mean = 22

Standard Deviation: 3.1

x = 29

a)

2.26

b)

16.45

c)

-2.26

d)

1.26

19.
What happens to the shape of a sampling distribution of sample means as n increases?
a)
It becomes narrower and bimodal.
b)
It becomes narrower and more normal.
c)
It becomes wider and skewed right. 
d)
It becomes wider and more normal. 
20.
At a particular college, 78% of all students are receiving some kind of financial aid.The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?
a)
 78% is a population and 72% is a sample.
b)
72% is a population and 78% is a sample
c)
78% is a parameter and 72% is a statistic
d)
72% is a parameter and 78% is a statistic

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